Impacts of Varied Injection Timing on Emission Levels, Combustion Efficiency, and Performance of Biodiesel Engines

Computational fluid dynamic (CFD) analysis is carried out for six different injection times to study combustion characteristics of diesel engines working with biodiesel fuel. Tables 1 and 2 show the engine specifications and biodiesel fuel characteristics. In this study, a single-cylinder, four-stroke diesel engine with direct injection has been run with biodiesel fuel under engine speed 1500 rpm (Figure 1). Biodiesel fuel extracted from soybean methyl ester was used. For combustion simulations within the engine, the ANSYS FLUENT software has been used. Furthermore, the major governing equations (mass, momentum, energy, and species) were solved using the three dimensions pressure-based implicit unsteady solver. Additionally, the finite volume strategy is employed to compute equation solutions during each time period. In this study, ANSYS FLUENT is based on the pressure correction strategy and employs the PISO algorithm. The momentum, energy, and turbulence equations were solved using a 2nd-order upwind differencing (UD) approach. Also, a model of premixed combustion was utilized to simulate the combustion. The equation of species transport and finite rate chemical reactions were combined with the injection of discrete phase to solve the species. In addition, the upwind scheme has been used for the model equation’s discretization. Concurrently, the RNG k- model was implemented to model turbulence predicated on. The collision model, along with the TAB breakup model, are applied to the spray [18]. Due to the difficulty of the problem, only a 60° sector of the model was defined utilizing 3D software, as shown in Figure 2. The Design Modeler ANSYS tool is used to model the in-cylinder geometry from the closed inlet valve to the open exhaust valve, and grid creation is performed for six different injection times at crank angles of 320,325,330,335,337 and 340 (Figures 2 and 3). Besides that, the flow field for simulation was a chamber of combustion (Figure 2), and the intake valve, exhaust valve, intake port, and exhaust port, were all neglected. 0.0006 kg/s biodiesel fuel was pumped into the end of the compression stroke for ignition.

Table 1. Specification of engine [19]

Table 2. Characteristics of fuel [20, 21]

2.1 Mechanism of chemical kinetic

The Ansys workbench /FLUENT program is employed to simulate biodiesel combustion. In this study, biodiesel fuel extracted from soybean methyl ester was used. The chemical reaction equation of biodiesel is [22, 23]:

$\begin{gathered}\mathrm{C}_{18.75} \mathrm{H}_{34.55} \mathrm{O}_2+26.3875 \mathrm{O}_2 \rightarrow 18.75 \mathrm{CO}_2+ 17.275 \mathrm{H}_2 \mathrm{O}+\mathrm{Heat}\end{gathered}$         (1)

$\mathrm{H}_2+0.5 \mathrm{O}_2 \leftrightarrow 2 \mathrm{H}_2$         (2)

$\mathrm{CO}+\mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{CO}_2+\mathrm{H}_2$         (3)

The emissions of NO are modeled through using extended Zeldovich mechanism. The three chemical formulas that comprise the extended Zeldovich reaction, also called thermal NO, are as follows [24]:

$\mathrm{N}+\mathrm{O}_2 \leftrightarrow \mathrm{O}+\mathrm{NO}$         (4)

$N+O H \leftrightarrow H+N O$         (5)

$N_2+O \leftrightarrow N+N O$         (6)

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Figure 1. The engine shape after drawing it with the ANSYS workbench program

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Figure 2. A combustion chamber shape with a 60° sector

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Figure 3. Combustion chamber meshing domain

2.2 Turbulence model

The turbulent flow was characterized by the variability of velocity field. The well-known RNG k- model was applied to simulate turbulence in this study [25]. The RNG k- model was created using a sophisticated statistical method. The RNG k- model was similar in format to the standard k- model, but it had the benefit of adding the impact of swirl, which was significant for ICE combustion analysis [26]. The transport formulas for the RNG k- Model are as follows:

$\frac{\partial}{\partial t}(\rho k)+\frac{\partial}{\partial x_i}\left(\rho k u_i\right)=\frac{\partial}{\partial x_i}\left[\left(\mu+\frac{\mu_t}{\sigma_k}\right) \frac{\partial k}{\partial x_j}\right]+P_k-p \epsilon$         (7)

$\frac{\partial}{\partial t}(\rho \epsilon)+\frac{\partial}{\partial x_i}\left(\rho \epsilon u_i\right)=\frac{\partial}{\partial x_i}\left[\left(\mu+\frac{\mu_t}{\sigma_\epsilon}\right) \frac{\partial \epsilon}{\partial x_j}\right]+C_{1 \epsilon} \frac{\epsilon}{k} p_\epsilon-C_{2 \epsilon}^* \rho \frac{\epsilon^2}{k}$         (8)

where, $C_{2 \epsilon}^*=C_{2 \epsilon}+\frac{C_\mu \eta^3\left(1-\frac{\eta}{\eta_o}\right)}{1+B \eta^3}$.

2.3 Combustion modeling

This method has been merged with species transports and finite percentage chemistry with streamlined chemistry reactions to predict biodiesel engine combustion characteristics. This method is based on the solving of equations of transport involving the mass fractions of species. The levels of the reactions that appeared as formulas in the species transport equations were also estimated using the Arrhenius rate prevalent expressions [25].

Equation of Arrhenius rate is:

$\dot{\mathrm{R}}_{i, r}=\Gamma\left(\ddot{\mathrm{v}}_{i, r}-\dot{\mathrm{v}}_{i, r}\right)\left(\prod_{i=1}^N\left[C_{i, r}\right]^{\dot{\eta}_{i, r}}-k_{b, r} \prod_{i=1}^N\left[C_{i, r}\right]^{\dot{v}_{i, r}}\right)$         (9)

r denotes the overall impact of third bodies on the reaction rate. This phrase can be written as:

$\Gamma=\sum_i^N \gamma_{i, r} C_i$         (10)

where, γ_i,r is the efficiency of the third body of j-th species in the r-th reaction.

$k_{i, r}=A_r T^{\beta r} e^{-E_r / R T}$         (11)

where,

A_r is a factor of a pre-exponential (consistent units).

Г is an exponent of temperature (dimensionless).

R is constant of a universal gas (J/kgmol-K).

E_r is the reaction's activation energy (J/kgmol).

2.4 Engine ignition modeling

In this research, the method of auto-ignition (model of Harden-burg) was the best option for simulating a direct-injection biodiesel engine. The following formula is the equation of transport for an ignition species Y_ig [25, 26]:

$\frac{\partial \rho Y_{i g}}{\partial t}+\nabla \cdot\left(\rho \vec{v} Y_{i g}\right)=\nabla \cdot\left(\frac{\mu_t}{S c_t} \nabla Y_{i g}\right)+\rho S_{i g}$         (12)

In which:

Y_ig is the radical species' mass fraction.

S_ctis Schmidt's turbulent number.

$\rho$ is the density of fluid (kg/m³).

S_igis the source expression for the combustion species.

μ_t is viscosity.

$v$ is the vector of absolute velocity (m/s).

2.5 Spray break up model

The TAB model was employed in this study. The TAB model was built on a comparison between the system of spring-mass and a deforming and oscillating droplet. In the current investigation, the distorting droplet impact was taken into consideration [22, 25]. A damped force oscillator is governed by the following equation:

$F-k x-d \frac{d x}{d t}=m \frac{d^2 x}{d t^2}$         (13)

where, the parameters of this equation and the displacement of the droplet center from its spherical location are determined from Taylor's analogy:

$\frac{F}{m}=C_F \frac{\rho g \mu^2}{\rho \operatorname{ir}}$         (14)

$\frac{\mathrm{k}}{\mathrm{m}}=\mathrm{C}_{\mathrm{k}} \frac{\rho}{\rho \mathrm{ir}^3}$         (15)

$\frac{\mathrm{d}}{\mathrm{m}}=\mathrm{C}_{\mathrm{d}} \frac{\mu_{\mathrm{i}}}{\rho \mathrm{lr}^2}$         (16)

where, ρ_i and ρ_a are the densities of discrete and continuous phases, σ is the surface tension of droplets, r is the radius of an undisturbed droplet, μ_i was the viscosity of the droplet and V_r is the droplet's relative velocity.

2.6 Droplet collision model

Droplet tracking is employed in the model of droplet collision to determine the number of droplet collisions and their findings in an algorithm-accurate way. The model is focused on O'Rourke's strategy, which presumes stochastic collision approximation. When two parcels of droplets collide an algorithm further establishes the type of collision. Only the outcomes of bouncing and coalescence are measured. The prediction of each result was determined using the number of collision Weber and match to the data of experimental. The Weber number was written as follows [25]:

$W_e=\frac{\rho V_r^2 l}{\sigma}$         (17)

where, V_r is the difference in speed between two parcels and l is the two parcels' average geometric diameter.

2.7 Initial and boundary conditions

The simulations initiate at 320 crank angle degrees before TDC and end at 420 crank angle degrees after TDC, covering the stroke of compression and combustion. In addition, the beginning pressure and temperature within the engine should be identified to provide beginning conditions in terms of the governing equations to be solved. Furthermore, the preliminary pressure is 15000000 Pa, while the temperature was 600C. The step of time for each degree of crank angle for the activities was 0.25, implying that four steps of time will be permitted to calculate one degree of crank angle. The small steps of time were chosen to avoid negative densities occurring throughout the computation.

This method has been merged with species transports and finite percentage chemistry with streamlined chemistry reactions to predict biodiesel engine combustion characteristics. This method is based on the solving of equations of transport involving the mass fractions of species. The levels of the reactions that appeared as formulas in the species transport equations were also estimated using the Arrhenius rate prevalent expressions [25].

2.8 Grid generation

Firstly, the mesh independence evaluation was primed for the AV1 (Kirloskar) diesel engine model. As shown in Figure 4 and Table 3, four various mesh sizes were generated. The simulation was performed for each mesh at a speed of 1500 rpm and the injection time at crank angle 340 to demonstrate the mesh independence test. The calculated cylinder pressure peak inside the chamber of combustion is shown in Figure 5. The results show no discernible difference in the results of pressure peak between the four mesh sizes. Meshing model 3 was selected based on the test of the mesh dependence because it provides extremely accurate findings while minimizing computation time.

Table 3. The mesh-independent test for the engine geometry

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Figure 4. The three-size different meshes

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Figure 5. Mesh independence verification outcome

2.9 Validation model

A single-cylinder combustion chamber model was created and simulated for verification. A numerical model of a 3D combustion chamber has been compared with the experimental model of Rajeesh et al. [19]. Comparisons have been made at 1500 rpm speed, a temperature of 300K, and using biodiesel fuel as an alternative to diesel fuel. The cylinder pressure obtained from the numerical analysis has been confirmed by the experimental results of Rajeesh et al. [19]. Figure 6 displays the in-cylinder pressure verification. In overall, simulated results seem to be in good agreement with experimental results at most points Rajeesh et al. [19].

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Figure 6. Verification of a single-cylinder combustion chamber model running under biodiesel fuel and at 2000 rpm engine speed